Use the Data Set from Appendix B to test the given claim....

Use the Data Set from Appendix B to test the given claim. Data Set 2 in Appendix $\mathrm{B}$ includes measured human body temperatures. Use the temperatures listed for 12 an on day 2 to test the common belief that the mean body temperature is $98.6^{\circ} \mathrm{F}$. Does that common belief appear to be wrong?

Use the Data Set from Appendix B to test the given claim.
Data Set 2 in Appendix $\mathrm{B}$ includes measured human body temperatures. Use the temperatures listed for 12 an on day 2 to test the common belief that the mean body temperature is $98.6^{\circ} \mathrm{F}$. Does that common belief appear to be wrong?

Key Concepts

P-value

The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value assuming the null hypothesis is true. It is used to determine the significance of the test result by comparing it against a predetermined significance level, thereby guiding the decision to reject or fail to reject the null hypothesis.

One-sample t-test

A one-sample t-test is used when testing a hypothesis about the mean of a normally distributed population when the sample size is small and the population standard deviation is unknown. In this context, it helps determine whether the sample mean significantly differs from the hypothesized value of 98.6°F.

Test Statistic

The test statistic quantifies the difference between the sample estimate and the hypothesized parameter value, scaled by the standard error of the estimate. For a one-sample t-test, it is computed using the sample mean, the hypothesized mean, and the sample standard deviation, and follows a t-distribution under the null hypothesis.

Statistical Hypothesis Testing

This is a process of making inferences about a population parameter based on sample data. It involves formulating a statement (the hypothesis) about the population parameter and then using sample data to test the validity of that statement, ultimately either rejecting or failing to reject the null hypothesis.

Null and Alternative Hypotheses

These are the two competing claims in hypothesis testing. The null hypothesis typically represents the status quo or a claim of no effect (in this case, that the true mean body temperature is 98.6°F), while the alternative hypothesis represents the claim that contradicts the null, such as the mean body temperature being different from 98.6°F.

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